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MathNet 2026 — Part 01 Question 42

Math Olympiad Vault · MathNet 2026 — Part 01

Question 42

Two boxes contain 65 balls of various sizes. Each ball is white, black, red or yellow. Each time we take five balls of the same color, at least two are the same size.
a. What is the maximum number of ball types that exist in the boxes? Two balls are considered of different types when they have different colors or sizes.
b. shows that there are at least three balls, which are in the same box, and which are of the same type.